On the decay of a light spinless particle into two photons

We analyze the effective couplings of a light, spinless, gauge-singlet particle ϕ to on-shell photons. Starting from the most general theory at the electroweak scale, which allows for CP-violating interactions suppressed by inverse powers of an ultraviolet scale Λ, we derive the corresponding low-energy effective theory valid below the GeV scale. Within this framework, we systematically expand the effective couplings of ϕ to on-shell photons in powers of small parameters. Working at the one-loop level, we retain terms at first order in 1/Λ. We incorporate both isospin-breaking effects and η–η′ mixing, and provide explicit expressions for the couplings up to first order in m²_ϕ/m²_η and m²_π/m²_η. As applications, we compute the decay rate of ϕ into two photons and illustrate our results in several physically motivated scenarios.